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As the rate of energy release from reaction decreases due to decrease of reactant concentrations, the heat loss to environment begins to be felt and peak in the temperature is reached. 8 Dimensionless temperature (u) as a function of dimensionless time (t) and parameter b assuming c ¼ 1 and g ¼ 5. environment surpasses the rate of energy generation owing to the reaction and the temperature continues to decline. 4. Increases in parameter g lead to slower reactions. 8 (plotted for the same c), it is possible to verify that at any given time, higher values of g lead to slower heating rates and lower temperatures.

Obviously, if endothermic (c < 0), the temperature would decrease and vice versa if exothermic (c > 0). 7 presents values for c ¼ 1. 5. 8 shows the effect of increasing parameter g, which is set as 5 while c is kept at 1. 5. 5. It is interesting to verify the following: 1. 5. 45); therefore, low values of c indicate slow reaction rates. 2. 6. As seen, for faster reactions, temperature rises faster and, for a given instant (t or t), it reaches higher values. 3. , when the heating device is not working and the temperature varies only because of exothermal reaction.

30 is always positive. 30) is not separable but can be solved by several methods. Among such methods, there is the method of variation of parameters described in Appendix B. It starts by trying a solution with the following form: u(t) ¼ u1 (t)u2 (t) (1:33) Here, u1 and u2 are functions of t. This maneuver does not impose any loss of generality. 33 introduces an extra degree of freedom. 34. On the other hand, such a condition should avoid restrictions to such a trivial solution u, or lead to unreal results.